Problem: Simplify the following expression: $ r = \dfrac{-10}{7} - \dfrac{-10}{-10n - 8} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10n - 8}{-10n - 8}$ $ \dfrac{-10}{7} \times \dfrac{-10n - 8}{-10n - 8} = \dfrac{100n + 80}{-70n - 56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-10}{-10n - 8} \times \dfrac{7}{7} = \dfrac{-70}{-70n - 56} $ Therefore $ r = \dfrac{100n + 80}{-70n - 56} - \dfrac{-70}{-70n - 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{100n + 80 + 70 }{-70n - 56} $ Distribute the negative sign: $r = \dfrac{100n + 80 + 70}{-70n - 56}$ $r = \dfrac{100n + 150}{-70n - 56}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{-50n - 75}{35n + 28}$